# ZADU: A Python Library for Evaluating the Reliability of Dimensionality Reduction Embeddings

arXiv: https://arxiv.org/abs/2308.00282 · HTML: https://mlsanity.com/paper/2308.00282/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 46 references that are in the map.
- First posted on arXiv 1 Aug 2023.

## Builds on (most cited first, 8 of 8)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [Measuring and Explaining the Inter-Cluster Reliability of Multidimensional Projections](https://mlsanity.com/paper/2107.07859/) (2021)
- [Uniform Manifold Approximation with Two-phase Optimization](https://mlsanity.com/paper/2205.00420/) (2022)
- [Feature Learning for Nonlinear Dimensionality Reduction toward Maximal Extraction of Hidden Patterns](https://mlsanity.com/paper/2206.13891/) (2022)
- [Sanity Check for External Clustering Validation Benchmarks using Internal Validation Measures](https://mlsanity.com/paper/2209.10042/) (2022)
- [Distortion-Aware Brushing for Reliable Cluster Analysis in Multidimensional Projections](https://mlsanity.com/paper/2201.06379/) (2022)

## Built on by (most cited first, 15 of 15)

- [Stop Misusing t-SNE and UMAP for Visual Analytics](https://mlsanity.com/paper/2506.08725/) (2025)
- [A Large-Scale Sensitivity Analysis on Latent Embeddings and Dimensionality Reductions for Text Spatializations](https://mlsanity.com/paper/2407.17876/) (2024)
- [Pattern or Artifact? Interactively Exploring Embedding Quality with TRACE](https://mlsanity.com/paper/2406.12953/) (2024)
- [Metric Design != Metric Behavior: Improving Metric Selection for the Unbiased Evaluation of Dimensionality Reduction](https://mlsanity.com/paper/2507.02225/) (2025)
- [Dataset-Adaptive Dimensionality Reduction](https://mlsanity.com/paper/2507.11984/) (2025)
- [GhostUMAP2: Measuring and Analyzing (r,d)-Stability of UMAP](https://mlsanity.com/paper/2507.17174/) (2025)
- [Understanding Bias in Perceiving Dimensionality Reduction Projections](https://mlsanity.com/paper/2507.20805/) (2025)
- [UMATO: Bridging Local and Global Structures for Reliable Visual Analytics with Dimensionality Reduction](https://mlsanity.com/paper/2508.16227/) (2025)
- [How Scale Breaks "Normalized Stress" and KL Divergence: Rethinking Quality Metrics](https://mlsanity.com/paper/2510.08660/) (2025)
- [MAPLE: Self-Supervised Learning-Enhanced Nonlinear Dimensionality Reduction for Visual Analysis](https://mlsanity.com/paper/2601.20173/) (2026)
- [Navigating High-Dimensional Backstage: A Guide for Exploring Literature for the Reliable Use of Dimensionality Reduction](https://mlsanity.com/paper/2506.14820/) (2025)
- [Why Can't I See My Clusters? A Precision-Recall Approach to Dimensionality Reduction Validation](https://mlsanity.com/paper/2509.04222/) (2025)
- [A Spectral Decomposition Framework for Multiscale Nonlinear Dimensionality Reduction](https://mlsanity.com/paper/2604.02535/) (2026)
- [Class Angular Distortion Index for Dimensionality Reduction](https://mlsanity.com/paper/2605.00637/) (2026)
- [Measuring Distortion in the Empty Regions of Dimensionality Reduction Scatterplots with the Gap Index](https://mlsanity.com/paper/2607.28324/) (2026)

## Abstract (arXiv)

Dimensionality reduction (DR) techniques inherently distort the original structure of input high-dimensional data, producing imperfect low-dimensional embeddings. Diverse distortion measures have thus been proposed to evaluate the reliability of DR embeddings. However, implementing and executing distortion measures in practice has so far been time-consuming and tedious. To address this issue, we present ZADU, a Python library that provides distortion measures. ZADU is not only easy to install and execute but also enables comprehensive evaluation of DR embeddings through three key features. First, the library covers a wide range of distortion measures. Second, it automatically optimizes the execution of distortion measures, substantially reducing the running time required to execute multiple measures. Last, the library informs how individual points contribute to the overall distortions, facilitating the detailed analysis of DR embeddings. By simulating a real-world scenario of optimizing DR embeddings, we verify that our optimization scheme substantially reduces the time required to execute distortion measures. Finally, as an application of ZADU, we present another library called ZADUVis that allows users to easily create distortion visualizations that depict the extent to which each region of an embedding suffers from distortions.